Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit: How Many Iterations Do We Need?

Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements. In this paper, we analyze the number of iterations required for the OMP algorithm to perform exact recovery of sparse signals. Our analysis shows that OMP can accurately recover all $K$-sparse signals within $\lceil 2.8 K \rceil$ iterations when the measurement matrix satisfies a restricted isometry property (RIP). Our result improves upon the recent result of Zhang and also bridges the gap between Zhang's result and the fundamental limit of OMP at which exact recovery of $K$-sparse signals cannot be uniformly guaranteed

Sparse Detection of Non-Sparse Signals for Large-Scale Wireless Systems

In this paper, we introduce a new detection algorithm for large-scale wireless systems, referred to as post sparse error detection (PSED) algorithm, that employs a sparse error recovery algorithm to refine the estimate of a symbol vector obtained by the conventional linear detector. The PSED algorithm operates in two steps: 1) sparse transformation converting the original non-sparse system into the sparse system whose input is an error vector caused by the symbol slicing and 2) estimation of the error vector using the sparse recovery algorithm. From the asymptotic mean square error (MSE) analysis and empirical simulations performed on large-scale systems, we show that the PSED algorithm brings significant performance gain over classical linear detectors while imposing relatively small computational overhead

Statistical Recovery of Simultaneously Sparse Time-Varying Signals from Multiple Measurement Vectors

In this paper, we propose a new sparse signal recovery algorithm, referred to as sparse Kalman tree search (sKTS), that provides a robust reconstruction of the sparse vector when the sequence of correlated observation vectors are available. The proposed sKTS algorithm builds on expectation-maximization (EM) algorithm and consists of two main operations: 1) Kalman smoothing to obtain the a posteriori statistics of the source signal vectors and 2) greedy tree search to estimate the support of the signal vectors. Through numerical experiments, we demonstrate that the proposed sKTS algorithm is effective in recovering the sparse signals and performs close to the Oracle (genie-based) Kalman estimator

Multipath Matching Pursuit

In this paper, we propose an algorithm referred to as multipath matching pursuit that investigates multiple promising candidates to recover sparse signals from compressed measurements. Our method is inspired by the fact that the problem to find the candidate that minimizes the residual is readily modeled as a combinatoric tree search problem and the greedy search strategy is a good fit for solving this problem. In the empirical results as well as the restricted isometry property (RIP) based performance guarantee, we show that the proposed MMP algorithm is effective in reconstructing original sparse signals for both noiseless and noisy scenarios.Comment: To appear in IEEE Transactions on Information Theor

Sparse Vector Coding for Ultra-Reliable and Low Latency Communications

Ultra reliable and low latency communication (URLLC) is a newly introduced service category in 5G to support delay-sensitive applications. In order to support this new service category, 3rd Generation Partnership Project (3GPP) sets an aggressive requirement that a packet should be delivered with 10^-5 packet error rate within 1 ms transmission period. Since the current wireless transmission scheme designed to maximize the coding gain by transmitting capacity achieving long codeblock is not relevant for this purpose, a new transmission scheme to support URLLC is required. In this paper, we propose a new approach to support the short packet transmission, called sparse vector coding (SVC). Key idea behind the proposed SVC technique is to transmit the information after the sparse vector transformation. By mapping the information into the position of nonzero elements and then transmitting it after the random spreading, we obtain an underdetermined sparse system for which the principle of compressed sensing can be applied. From the numerical evaluations and performance analysis, we demonstrate that the proposed SVC technique is very effective in URLLC transmission and outperforms the 4G LTE and LTE-Advanced scheme.Comment: To appear in IEEE Transactions on Wireless Communications. Copyright 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other use

Optimal Power Control for Transmitting Correlated Sources with Energy Harvesting Constraints

We investigate the weighted-sum distortion minimization problem in transmitting two correlated Gaussian sources over Gaussian channels using two energy harvesting nodes. To this end, we develop offline and online power control policies to optimize the transmit power of the two nodes. In the offline case, we cast the problem as a convex optimization and investigate the structure of the optimal solution. We also develop a generalized water-filling based power allocation algorithm to obtain the optimal solution efficiently. For the online case, we quantify the distortion of the system using a cost function and show that the expected cost equals the expected weighted-sum distortion. Based on Banach's fixed point theorem, we further propose a geometrically converging algorithm to find the minimum cost via simple iterations. Simulation results show that our online power control outperforms the greedy power control where each node uses all the available energy in each slot and performs close to that of the proposed offline power control. Moreover, the performance of our offline power control almost coincides with the performance limit of the system.Comment: 15 pages, 12 figure

Greedy Sparse Signal Recovery with Tree Pruning

Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the support (index set of nonzero elements) of the sparse signals. Well-known drawback of the greedy approach is that the chosen candidate is often not the optimal solution due to the myopic decision in each iteration. In this paper, we propose a greedy sparse recovery algorithm investigating multiple promising candidates via the tree search. Two key ingredients of the proposed algorithm, referred to as the matching pursuit with a tree pruning (TMP), to achieve efficiency in the tree search are the {\it pre-selection} to put a restriction on columns of the sensing matrix to be investigated and the {\it tree pruning} to eliminate unpromising paths from the search tree. In our performance guarantee analysis and empirical simulations, we show that TMP is effective in recovering sparse signals in both noiseless and noisy scenarios.Comment: 29 pages, 8 figures, draftcls, 11pt

Structured Compressive Sensing Based Spatio-Temporal Joint Channel Estimation for FDD Massive MIMO

Massive MIMO is a promising technique for future 5G communications due to its high spectrum and energy efficiency. To realize its potential performance gain, accurate channel estimation is essential. However, due to massive number of antennas at the base station (BS), the pilot overhead required by conventional channel estimation schemes will be unaffordable, especially for frequency division duplex (FDD) massive MIMO. To overcome this problem, we propose a structured compressive sensing (SCS)-based spatio-temporal joint channel estimation scheme to reduce the required pilot overhead, whereby the spatio-temporal common sparsity of delay-domain MIMO channels is leveraged. Particularly, we first propose the non-orthogonal pilots at the BS under the framework of CS theory to reduce the required pilot overhead. Then, an adaptive structured subspace pursuit (ASSP) algorithm at the user is proposed to jointly estimate channels associated with multiple OFDM symbols from the limited number of pilots, whereby the spatio-temporal common sparsity of MIMO channels is exploited to improve the channel estimation accuracy. Moreover, by exploiting the temporal channel correlation, we propose a space-time adaptive pilot scheme to further reduce the pilot overhead. Additionally, we discuss the proposed channel estimation scheme in multi-cell scenario. Simulation results demonstrate that the proposed scheme can accurately estimate channels with the reduced pilot overhead, and it is capable of approaching the optimal oracle least squares estimator.Comment: 16 pages; 12 figures;submitted to IEEE Trans. Communication

Joint Channel Training and Feedback for FDD Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is widely recognized as a promising technology for future 5G wireless communication systems. To achieve the theoretical performance gains in massive MIMO systems, accurate channel state information at the transmitter (CSIT) is crucial. Due to the overwhelming pilot signaling and channel feedback overhead, however, conventional downlink channel estimation and uplink channel feedback schemes might not be suitable for frequency-division duplexing (FDD) massive MIMO systems. In addition, these two topics are usually separately considered in the literature. In this paper, we propose a joint channel training and feedback scheme for FDD massive MIMO systems. Specifically, we firstly exploit the temporal correlation of time-varying channels to propose a differential channel training and feedback scheme, which simultaneously reduces the overhead for downlink training and uplink feedback. We next propose a structured compressive sampling matching pursuit (S-CoSaMP) algorithm to acquire a reliable CSIT by exploiting the structured sparsity of wireless MIMO channels. Simulation results demonstrate that the proposed scheme can achieve substantial reduction in the training and feedback overhead

On the Fundamental Recovery Limit of Orthogonal Least Squares

Orthogonal least squares (OLS) is a classic algorithm for sparse recovery, function approximation, and subset selection. In this paper, we analyze the performance guarantee of the OLS algorithm. Specifically, we show that OLS guarantees the exact reconstruction of any $K$-sparse vector in $K$ iterations, provided that a sensing matrix has unit $\ell_{2}$-norm columns and satisfies the restricted isometry property (RIP) of order $K+1$ with \begin{align*} \delta_{K+1} &<C_{K} = \begin{cases} \frac{1}{\sqrt{K}}, & K=1, \\ \frac{1}{\sqrt{K+\frac{1}{4}}}, & K=2, \\ \frac{1}{\sqrt{K+\frac{1}{16}}}, & K=3, \\ \frac{1}{\sqrt{K}}, & K \ge 4. \end{cases} \end{align*} Furthermore, we show that the proposed guarantee is optimal in the sense that if $\delta_{K+1} \ge C_{K}$, then there exists a counterexample for which OLS fails the recovery